The Duck-curve


The Duck-curve is the first of a series of new fractals I have found.
Here are step 0 and step 1 of the Duck-curve:
0 1
The next two steps:
2 3
In step 3 the curve touches itself, creating two enclosed figures. With some imagination, you can recognise a swimming duck in such a figure: a Duck-figure.

4 5
In the next steps more and more Duck-figures are added, smaller ones and in each step more different sizes fit together.

6 7

There are many variants of the Duck-curve. If you are interested, see page Variants of Duck-curve.

The Duck-figure


On the left you see a copy of the Duck-figure. The right image shows the Duck-figure consists of four isosceles and similar triangles.
Eend-figuur Eend-figuur2

Tesselations with Duck-figures


Because the Duck-figures of different sizes fit together so well in the Duck-curve, I have tried to build other configurations.
Here are some examples (in too bright colours):

Vlakvulling 2v2   Vlakvulling 3v1

Vlakvulling 4v3   Vlakvulling 4v1


The work submitted for Bridges 2025:

Vlakvulling 4v3a